Conditions for inception of relativistic runaway discharges in air

Terrestrial gamma-ray flashes are linked to growth of long bidirectional lightning leader system consisting of positive and stepping negative leaders. The spatial extent of streamer zones of a typical lightning leader with tip potential exceeding several tens of megavolts is on the order of 10 to 100 meters. The photoelectric absorption of bremsstrahlung radiation generated by avalanching relativistic runaway electrons occurs efficiently on the same spatial scales. The intense multiplication of these electrons is triggered when the size of the negative leader streamer zone crosses a threshold of approximately 100 meters (for sea-level air pressure conditions) allowing self-replication of these avalanches due to the upstream relativistic electron seeds generated by the photoelectric absorption. The model results also highlight importance of electrode effects in interpretation of X-ray emissions from centimeter to meter long laboratory discharges, in particular, a similar feedback effect produced by generation of runaway electrons from the cathode material.